منابع مشابه
Amalgamations of Lattice Ordered Groups
The author considers the problem of determining whether certain classes of lattice ordered groups (¿-groups) have the amalgamation property. It is shown that the classes of abelian totally ordered groups (ogroups) and abelian /-groups have the property, but that the class of ¿-groups does not. However, under certain cardinality restrictions one can find an ¿-group which is the "product" of /-gr...
متن کاملConvex $L$-lattice subgroups in $L$-ordered groups
In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...
متن کاملLattice-ordered reduced special groups
Special groups [M. Dickmann, F. Miraglia, Special Groups : Boolean-Theoretic Methods in the Theory of Quadratic Forms, Memoirs Amer. Math. Soc., vol. 689, Amer. Math. Soc., Providence, RI, 2000] are a first-order axiomatization of the theory of quadratic forms. In Section 2 we investigate reduced special groups (RSG) which are a lattice under their natural representation partial order (for moti...
متن کاملFree abelian lattice-ordered groups
Let n be a positive integer and FA`(n) be the free abelian latticeordered group on n generators. We prove that FA`(m) and FA`(n) do not satisfy the same first-order sentences in the language L={+,−, 0,∧,∨} if m 6= n. We also show that Th(FA`(n)) is decidable iff n ∈ {1, 2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices. A. M. S. C...
متن کاملPermutational Products of Lattice Ordered Groups
Let H be a group, let {G(: i e 1} be a set of groups and, for each i, let 9t be a a monomorphism: H -* Gt, with H9t = Hi. We call such a system of groups and monomorphisms an amalgam and denote it by [G{; H; 9,; / / , ] . By an embedding of the amalgam into a group G is meant a set of monomorphisms (p; : G; -*• G such that 9i<pi = 0j<Pj-, for all i,j and G,<P; n Gjcpj — H9k<pk, for all i,j, k. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1972
ISSN: 0002-9947
DOI: 10.2307/1996346